Piezoelectric system



Aug" 17, 1948. c. w. FRANKLIN PIEZOELECTRIC SYSTEM 2 Sheets-Sheet 1Filed July 18, 1945 1943- c. w. FRANKLIN 2,447,061

PIEZOELECTRIC SYSTEM Filed July 18, 1945 2 Sheets-Sheet 2 Patented Kug.17, I948 PIEZOELECTRIC SYSTEM Constance W. Franklin, Belmont, Mass,assignor to Cambridge Thermionic Corporation, Cambridge, Mass, acorporation of Massachusetts Application July 18, 1945, Serial No.605,665

11 Claims. 1

The present invention relates to piezo electric systems, and moreparticularly to supersonic systems incorporating a piezo electriccrystal body which is peculiarly cut for greater eifectiveness in suchsystems.

The use of the piezo electric effect in oscillators for generating highfrequency sound waves in fluids, either gaseous or liquid, of anappropriately selected and shaped body of piezo electric material servinas a wave emitter upon being subjected to an oscillatin electric fieldis well known. Such sound waves have various practical uses. such as inthe physical field for heating, signaling, sounding or degassingpurposes; in the chemical field for purposes of emulsification andacceleration of reaction; and in the biological field for sterilizing.Most of these uses necessarily call for an energy output of maximumintensity, whereas the crystal body, as generator of such oscillation,inherently introduces limits in this respect due to its size as well asits dielectric and mechanical properties. Most of the above mentioneduses also call for an optimum distance of effectively maintainedintensity, which requirement involves minimum spread of the beam angleof the supersonic vibration, in order to concentrate or focus it at adesired point or other predetermined locus of application.

It has been proposed to obtain better results in the above respects byusing crystal shells with concentrically spherical surfaces insteadofthe customary parallel plane surfaces; compare, for example, thearticle of L. W. Labaw in The J ournal of the Acoustical Society ofAmerica, volume 16, No. 4, April 1945, pages 237 to 245. Such crystalshells actually do produce a vibratory beam which is thrown toward afocus of fairly strong amplitude instead of being projected with thespread of five to seven degrees that is produced by conventional planecrystals. However, these preyiously proposed curved crystals do notafforda consistent improvement in efliciency, in the above-mentionedrespects, over that of equivalent plane crystals. This failure becomesincreasingly apparent when the radius of curvature of the shell isdecreased while its cross measurement is maintained constant.

It is the main object of the present invention to provide a piezoelectric oscillator system which includes a crystal cut to securemaximum emciency of translation of electrical into mechanical energy andin its application to supersonic systems, to provide optimum sound waveoutput due to large oscillation amplitude and energy concentration forall radii and all curvatures. Other objects are to provide a crystal ofthe abovementioned desirable qualities, derived from a given body ofpiezo electric material, and to provide a method of cutting such acrystal according to the requirements of the invention.

In one of its aspects the invention employs, in an oscillator device ofthe above-mentioned type, a pulsating element which is cut from a piezoelectric crystal and which has sections with boundaries that are curvedin a fixed geometric relation to the characteristic axes of the crystalfrom which the element is cut, the dimensions which control thefrequency at which each elementary portion of the crystal vibrates in agiven electric field bein varied through these sections as a function ofthe relatio of the boundaries of the sections to the characteristicaxes, in such a way that the pulse frequency in an electric field issubstantially uniform throughout the element.

In another aspect, the invention contemplates the use, in supersonicsystems, of piezo electric elements the thickness of which varies insuch a manner that the pulsating frequencies in a given oscillatoryfield are the same for each elementary portion of the crystal, thesurfaces of the crystal having peculiarly varying inclinations to thecharacteristic axes of the crystal, such as to provide a region ofmaximum vibratory amplitude at a given spatial relation to the crystal.

In still another aspect, a feature of the invention concerns acup-shaped crystal shell, one of whose surfaces is substantiallyspherical whereas the other surface, preferably the outer surface, isbi-symmetrically curved so as to provide at two opposite points of therim of the crystal regions of minimum thickness, and therebetween twoopposite regions of maximum thickness, these regions being particularlyoriented with respect to the characteristic axes of the crystal so as toprovide the above-mentioned uniformity of frequency throughout thewave-emitting crystal surface, regardless of the relation of thatsurface to the directional properties of the peizo electric materialfrom which the shell is cut.

Another feature of the invention is a preferred way of cutting a blank,oriented in accordance with the teaching of the invention, from a rawcrystal, so as to facilitate the shaping of the crystal in its 'finalform; and still another feature is a method of manufacture, whichreduces delicate hand work in shaping the final crystal to a minimum.

These and other objects, aspects and features will be apparent from thefollowing description of an embodiment illustrating the novel charac- 3teristics of the invention. This description refers to drawings in whichFig. 1 is a diagram representing the relation of the shape and structureof a piezo electric shell according to the invention to the axes of thecrystal from which it is cut;

Fig. 2 graphically represents the modulus of elasticity as a function ofthe angle in the ZY plane of the crystal;

Fig. 3 is a plan view of a crystal shell out according to the invention;

Fig. 4 is an isometric view of a shell according to Fig. 3 with aquadrant removed on line 444 of Fig. 3;

Fig. 5 is a diagram illustrating the manner in which the blank for ashell according to Figs. 3 and 4 is cut from a quartz crystal;

Fig. 6 is a diagrammatic cross section through a crystal according tothe invention, at one manufacturing stage;

Fig. 7 is an isometric view similar to Fig. 4, of the crystal at thatstage; and

Fig. 8 is a schematic representation of supersonic apparatusincorporating a shell according to the invention.

By way of example the computation, manufacture and use, according to theinvention, of an X-cut quartz shell of 30 opening and with an innerspherical surface of 4 cm. radius will be described, but it isunderstood that the invention is limited neither to the axes relation,the particular curvature of the vibration-emitting surface, thematerial, nor the width of opening of the oscillating element. Forexample, the shell may be shaped with particular relation to the A-Ccut, it may have the shape of a cylinder for producing a line instead ofa point of focus, or piezoelectric material other than quartz, such asRochelle salt might be used, and the shell will have smaller or largeropenings and radii in accordance with the purpose to which thispulsating element is to be put.

The first step in manufacturing a crystal element according to theinvention is the determination of the distribution of the modulus ofelasticity over the crystal shell, as dependent on the orientation ofthe shell apex to the characteristic axes of the crystal.

In the present embodiment, as above indicated, the relation of the shellshape as defined by its apex is the one indicated in Fig. 1. In thisfigure X, Y and Z are the principal axes (right handed) of the quartzcrystal. a is the apex of the shell, the inner surface of which iscentered at O, and each peripheral point P of which lies on a line Rthrough 0. It will be evident that in this instance the wave propagationwill proceed along lines through 0 as focus, the outermost of whichlines are the above-mentioned lines R.

The computation of the modulus of elasticity along the shell rim followsin its initial stages the classical procedure as, for example, set forthby W. P. Mason in The Bell System Technical Journal, volume YXII, No. 2,July 1943, pages 178 to 223, with particular reference also to the workof R. Bechmann mentioned in footnote 12 of this article.

This procedure is based on the fact that any anisotropic body has for atransmission frequency in any selected direction three speeds ofpropagation whose values depend upon the direction of the excitingdisturbance and upon the relation of the selected direction to thecharacteristic axes of the crystal.

In accordance with this method of computation, the following equation isset up:

M1 0 M2 M3 M3 23 M3 C where M1 011 ms 55 20507771771 22= 60 11 't C55 5cA 055 055 33 M2 205m 12 068) lm M3 13 55) fifl M3 C5512 055772 (013 055)in and, with 1/1 and 0 positive in counterclockwise direction,

l=cos t cos 0 m=sin 11/ n=cos t sin 0 In these equations, C is aconstant or multiplicator which furnishes in the manner to be shownbelow the modulus values in direction R around the circumference of theshell under consideration; cm are the regular moduli of elasticity inthe direction of axes X, Y, Z; M the transformed moduli corresponding toa disturbance in an arbitrarily selected propagation direction ofspecified relation to X, Y, Z, here in directions R; Z, 171, n thedirection cosine values of the propagation direction defined by angles 0and 0 which determine the location of R relatively to the XZ and XYplanes, as indicated in Fig. 1.

Taking for Clj the values obtainable from standard works in this fieldfor example the above-mentioned article by W. P. Mason, the followingvalues for M5 in 10 dynes/em. are obtained.

A -85.1 cos t cos 0+39.l sin 57.1 cos ,0 sin 916.8 sin 1/ sin 0 A =39.lcos it cos 0+85.1 sin b-l- 57.1 cos b sin 6+ 16.8 sin b sin 0)\33=57.1COS2 t cos (9+57.1sin 0+ 105.3 cos 1,0 sin 0 A =16.8 cos t cos9l6.8 sin 7,11-

35.6 sin 0 sin 0 In order to compute these values, the trigonometriccomponents thereof have to be expressed in terms of R, the directions ofpropagation at the shell rim. In the present example these directionsare defined by one-half of the shell opening angle, namely 15, andspherical angle A, subtended at the apex of the shell by theintersection of the shell with the XZ plane, and the intersection of theshell with a plane through axis X and that point P of the shellperiphery which is under consideration; compare also Fig. l.

new on In these terms, the above-mentioned trigonometric components ofequation (2) are as follows:

sin b==sin A sin 15 cos it cos =cos 15 cos i// sin 0=cos A sin 15 sin #1sin 0=sin A sin 15 cos ll sin 6=cos A sin (30) sin 0 cos 0=Sil1 A sin(30) Writing the determinant given aboveunder (1) in the form (MiMaMsx12 13 23 115 141 O the factors according to Equation 2 are obtainedwith the aid of Equation 3.

Using these factors, the cubic function (4), and its derivative inNewtons method of approximate solution, consecutive approximations C0,C1, 02, etc., are set up, which values rapidly converge to an accuratesolution.

Having solved the cubic equation and thus obtained the C constants indirection R for a given value of A, the solution for a nearby value isreadily obtained by using next, for the first value of C, the valuecorresponding to the previous value of A. In this manner, there can beno doubt that the variations of the same root are obtained and that allthe values of C correspond to equivalent wave-fronts in the shell.

In this manner these values of the 0 factors, as varying around thecircumference of the 30 X-cut shell, are obtained. For the presentpurpose, these values are plotted in the form of a curve, given in Fig.2, which is self-explanatory.

It will be observed that the 0 value repeats itself for Ai180, whichcharacteristic is inherent in the nature of the cubic equation fromwhich these values are derived. It will further be observed that, forthe example in question, the C value and hence the modulus of elasticityhas double symmetry about the perpendicular lines for which A lies 57from +Z in the direction of Y and for which A lies 33 from +Z towardWith the distribution of the modulus of elasticity over the shell rimbeing known, the thickness of the latter can now be computed as follows!The frequency constant in kilocycles per second per mm. thickness isgiven by the formula wherein C is the above obtained factor, and d thedensity of quartz, namely 2.654 g./cc. For the apex of the shell,C'=c1i=85.1, and hence the frequency constant is 2831 at that point. Thefrequency constant divided by the thickness t at the point in question,which was assumed to be 2 mm. gives the natural frequency as 1416kc./sec. at the apex.

Taking now from the curve according to Fig. 2, the value of C minimum,we obtain for that point a frequency constant of 2779. Calculating fromformula (6) the thickness necessary to provide at that point the samenatural frequency which prevails at the apex, namely 1416 kc./sec., itis found the maximum C value of 101.4, we obtain a frequency constant of3090 and a corresponding maximum dimension of m=2.183 mm., correspondingto the frequency of 1416 kc./sec.

It will now be evident that the moduli of elasticity can similarly becomputed for every point of the shell, for example by assuming, insteadof the maximum spread of 15 on each side of the apex, intermediateangles, for example of 5 and 10, and computing for these angles curvessimilar to that shown in Fig. 2. The shell thickness for any point canthen be computed as above indicated for the minimum and maximumthicknesses. A crystal cut and dimensioned according to the abovecomputation is indicated in Figs. 3 and 4. These figures indicate theapex, maximum and minimum thicknesses, and the co-relation of thesevalues to the characteristic axes of the shell.

The manner of manufacturing a crystal having the characteristicsindicated in Figs. 3 and 4 will now be described.

The original blank is cut from the quartz crystal as indicated in Fig.5, which shows the maximum and minimum A angles measured in the YZplane, as derived from the chart of Fig. 2. The axes of symmetry of theblank are indicated in Fig. 5 at M and N. After having cut the blank asindicated in Fig. 5, the lens grinder marks the XM plane with deep sawmarks on both XN faces as indicated at s of Fig. 5. The apex is markedon the blank, and the lens grinder is given the radii of curvature ofthe blank in its second or envelope stage, obtained as follows.

The inner surface is spherical in its final shape, with a radius ofcurvature, as above pointed out, of 4 cm., and the maximum edgethickness is m=2.183 mm. Referring now to Fig. 6 where these data areindicated, the radius of the spherical envelope of the final outersurface is obtained from the relations:

h==4.815 cm.

The first step in grinding of the shell will therefore be the productionof a lens 2.025 mm. thick at the apex, the extra thickness in excess of2 mm. being allowed for possible grinding corrections, and slightly inexcess of 2.183 mm. at the edge, by using an inner matrix of 4 cm. andouter matrix of 4.8147 cm. radius. The above mentioned saw cuts will,after this operation, be reduced to edge nicks and might even bealtogether lost, in which case the Y and Z directions can be recoveredaccording to conventional methods from the knowledge of the X axis,defined and preserved by the apex. Fig. 7, which corresponds to Fig. 4,shows the blank at this stage.

The crystal should now be checked for twinning before proceeding to themore laborious and expensive final stage, which consists of flatteningthe outer surface in the direction of the minima. After verificationthat the shell is untwinned, a mark is applied running from the apex tothe ends of the grooves 8, thus indicating the maxima axis M. The minimadirection N perpendicular to the maxima axis M is also marked,conveniently in a different color.

The lens grinder now cuts the edge of the blank so that it is normal tothe inner surface and which is then thinned from the outside along the Naxis until the dimension 11:1.964 cm. is reached at the end of the Nline, on the edge of the shell, shading this dimension over the entireshell to figures furnished him, until the shape indicated in Figs. 3 and4 is reached.

Fig. 8 indicates supersonic apparatus incorporating a shell according toFigs. 3 and 4. In Fig. 8, numeral I indicates a conventional oscillatorcircuit, for example a stabilized, amplitude limited Hartley oscillatorfeeding into an amplifier II. The shell I5 may be supported on a leadblock holder l6 connected to one output terminal ll of the amplifier.Near the rim of the crystal l5 rests a copper ring l8, connected to theother terminal IS. The entire vibrating unit may be immersed in a tank20 containing insulating fluid 2|. When the oscillating field is appliedto electrodes I6 and 18, the shell vibrates through its entire bodyuniformly at the selected frequency, the vibration energy beingconcentrated at focus 0. The specimen to be treated, indicated in Fig. 8by a test tube 25, is held in the focus by appropriate means dependingupon the particular use to which the system is put.

It should be understood that the present disclosure is for the purposeof illustration only and that this invention includes all modificationsand equivalents which fall within the scope of the appended claims.

I claim:

1. In an oscillator device of the type described a pulsating element cutfrom piezo electric material with sections having curved boundaries infixed geometric relation to the characteristic axes of said material,the frequency controlling dimension of the element varying through saidsections with varying relation of said boundaries to said axes accordingto the mathematical function which defines the condition that saidelement furnishes in an oscillating electric field a pulse frequencywhich is substantially uniform throughout the element.

2. In an oscillator device of the type described a pulsating element cutfrom piezo electric material with sections having curved boundaries infixed geometric relation to the characteristic axes of said material,one boundary being curved to propagate mechanical vibrationssubstantially in predetermined directions and the second boundary beingcurved to provide frequency controlling dimensions of the element whichvary through said sections with varying relation of said boundaries tosaid axes according to the mathematical function which defines thecondition that said element furnishes in a given oscillating electricfield a pulse frequency which is substantially uniform throughout theelement,

3. In an oscillator device of the type described a pulsating element cutfrom piezo electric material with sections having curved boundaries infixed geometric relation to the characteristic axes of said materiaLoneboundar being curved to propagate mechanical vibrations substantially inpredetermined directions and the second boundary being curved to definewith said first boundary thicknesses of said sections which vary throughsaid element with varying direction and modulus of elasticity asdependent upon direction according to the mathematical function whichdefines the condition that said element furnishes in a given oscillatingelectric field frequency responses in said directions which aresubstantially uniform over said propagating boundary.

4. In an oscillator device of the type described a shell shapedpulsating element cut from piezo electric material with sections havingcurved boundaries in fixed geometric relation to the characteristic axesof said material, the concave boundary being spherical and the convexboundary being curved to provide frequency controlling dimension of theelement which vary through said sections with varying relation of saidboundaries to said axes according to the mathematical function whichdefines the condition that said element furnishes in a given oscillatinelectric field a pulse frequency which is substantiall uniformthroughout the element.

5. A cup-shaped shell of piezo electric material for generatingmechanical vibration while pulsating in an electric field, having onesurface which is substantially spherical whereas the other surface iscurved to define with said first surface two points of minimum thicknessat two regions of the rim of said shell and two points of thickness attwo regions between said minimum thickness regions, the thicknesses ofsaid shell gradually varying between the apex of said shell and saidpoints, and between said points, and said points being orientedregarding the characteristic axes of said material and the direction ofsaid field to provide pulsation at substantially uniform frequency ofsaid shell while in said field.

6. A cup-shaped shell of piezo electric material for generatingmechanical vibration while pulsating in an electric field, having aninner substantially spherical surface whereas the outer surface iscurved with two points of minimum thickness at two opposite regions ofthe rim of said shell and two points of maximum thickness at twoopposite regions between said minimum regions, the thicknesses of saidshell gradually varying between the apex of said shell and said points,and between said points, and said points being oriented regarding thecharacteristic axes of said material and the direction of said field toprovide pulsation at substantially uniform frequency of said shell whilein said field.

7. A cup-shaped shell of piezo electric material for generatingmechanical vibration while pulsating in an electric field, having anapex region of predetermined thickness, one surface which issubstantially spherical whereas the other surface is curved towards twoperipheral regions in which the shell is thinner than in said apexregion and two peripheral regions in which the shell is thicker than insaid apex region and located between said thinner regions, thethicknesses of said shell gradually varying between said apex region andsaid peripheral region and increasing gradually from minimum to maximumthickness along said periphery, and said regions being orientedregarding the characteristic axes of said material and the direction ofsaid field to provide pulsation at substantially uniform frequency ofsaid shell while in said field.

8. A cup-shaped shell of piezo electric material for generatingmechanical vibration while pulsating in an electric field, having onesurface which is substantiall spherical whereas the other surface isbisymmetrically curved with two points of minimum thickness at twoopposite regions of the rim of said shell and two points of maximumthickness at two opposite regions between said minimum thicknessregions, the thicknesses of said shell gradually varying between theapex of said shell and said points and increasing gradually from minimumto maximum thickness along said rim and said points being orientedregarding the characteristic axes of said material and the direction ofsaid field to provide pulsation at substantially uniform frequency ofsaid shell while in said field.

9. A cup-shaped shell of piezo electric material for generatingmechanical vibration while pulsating in an electric field, having anapex region of given thickness, an inner surface which is substantiallyspherical whereas the outer surface is bisymmetrically curved with twopoints of minimum thickness smaller than said apex thickness at twoopposite regions of the rim of said shell and two points of maximumthickness greater than the apex thickness at two opposite regionsbetween said minimum regions, the thicknesses of said shell graduallyvarying between said apex region and said points and increasinggradually from minimum to maximum thickness along said rim and saidpoints being oriented regarding the characteristic axes of said crystalmaterial and the direction of said field to provide pulsation atsubstantially uniform frequency of said shell while in said field.

10. In the art of manufacturing a curved body of piezo electric materialhaving an apex of given thickness and geometric relation to acharacteristic axis of said material and thickness dimensions varyingfrom said apex towards a region which is thicker, and a region which isthinner than said apex, said regions defining lines of predeterminedinclination relatively to two characteristic axes of said material: themethod which comprises cutting from said material a block having a facewhich is substantially perpendicular to said apex axis and a face whichis substantially parallel to one of said lines, grinding inner and outersurfaces of said body to 10 envelop said apex and said thicker regionportion, and thinning said body from said apex and said thicker regiontowards said thinner regions while preserving said apex axis, until saidshell conforms to said dimensions.

11. In the art of shaping a shell of piezo electric material having anapex of given thickness and geometric relation to a characteristic axisof said material and shell thickness dimensions which vary from saidapex towards two opposite rim regions which are thicker and two rimregions oppositely therebetween which are thinner than said apex, saidopposite regions defining lines substantially within the plane of twoother characteristic axes of said material and in predetermined angularrelation to said axes: the method which comprises cutting from saidmaterial a substantially parallelepipedal block two of whose faces aresubstantially parallel to said plane whereas pairs of oppositely locatedones of said other faces are substantially parallel to respective onesof said lines; marking each face of one of said pairs to indicate thedirection of one of said lines; spherically grinding inner and outershell surfaces to envelop said apex and said thicker regions; and guidedby said marking thinning said shell from said apex and said thickerregions towards said thinner regions, until said shell conforms to saiddimensions.

The following references are of record in the file of this patent:

FOREIGN PATENTS Number Country Date Germany Dec. 24, 1937

